CF1328E.Tree Queries

You are given a rooted tree consisting of $n$ vertices numbered from $1$ to $n$. The root of the tree is a vertex number $1$.

A tree is a connected undirected graph with $n-1$ edges.

You are given $m$ queries. The $i$-th query consists of the set of $k_i$ distinct vertices $v_i[1], v_i[2], \dots, v_i[k_i]$. Your task is to say if there is a path from the root to some vertex $u$ such that each of the given $k$ vertices is either belongs to this path or has the distance $1$ to some vertex of this path.

你将得到一棵包含 $n$ 个顶点（编号从 $1$ 到 $n$）的有根树，树的根节点为顶点 $1$。

树是一种具有 $n-1$ 条边的连通无向图。

你将收到 $m$ 个查询。第 $i$ 个查询包含一个由 $k_i$ 个互不相同的顶点 $v_i[1], v_i[2], \dots, v_i[k_i]$ 组成的集合。你的任务是判断：是否存在一条从根节点到某个顶点 $u$ 的路径，使得给定的 $k_i$ 个顶点中的每一个，要么位于该路径上，要么与该路径上的某个顶点的距离恰好为 $1$。

The first line of the input contains two integers $n$ and $m$ ($2 \le n \le 2 \cdot 10^5$, $1 \le m \le 2 \cdot 10^5$) — the number of vertices in the tree and the number of queries.

Each of the next $n-1$ lines describes an edge of the tree. Edge $i$ is denoted by two integers $u_i$ and $v_i$, the labels of vertices it connects $(1 \le u_i, v_i \le n, u_i \ne v_i$).

It is guaranteed that the given edges form a tree.

The next $m$ lines describe queries. The $i$-th line describes the $i$-th query and starts with the integer $k_i$ ($1 \le k_i \le n$) — the number of vertices in the current query. Then $k_i$ integers follow: $v_i[1], v_i[2], \dots, v_i[k_i]$ ($1 \le v_i[j] \le n$), where $v_i[j]$ is the $j$-th vertex of the $i$-th query.

It is guaranteed that all vertices in a single query are distinct.

It is guaranteed that the sum of $k_i$ does not exceed $2 \cdot 10^5$ ($\sum\limits_{i=1}^{m} k_i \le 2 \cdot 10^5$).

输入的第一行包含两个整数 $n$ 和 $m$（$2 \le n \le 2 \cdot 10^5$，$1 \le m \le 2 \cdot 10^5$）—— 分别表示树中顶点的数量和查询的数量。

接下来的 $n-1$ 行每行描述树中的一条边。第 $i$ 条边由两个整数 $u_i$ 和 $v_i$ 表示，即该边所连接的两个顶点的编号（$1 \le u_i, v_i \le n$，且 $u_i \ne v_i$）。

保证所给定的边构成一棵树。

接下来的 $m$ 行描述各个查询。第 $i$ 行描述第 $i$ 个查询，首先是一个整数 $k_i$（$1 \le k_i \le n$）—— 表示当前查询中顶点的数量；随后是 $k_i$ 个整数：$v_i[1], v_i[2], \dots, v_i[k_i]$（$1 \le v_i[j] \le n$），其中 $v_i[j]$ 表示第 $i$ 个查询中的第 $j$ 个顶点。

保证单个查询中所有顶点互不相同。

保证所有 $k_i$ 的总和不超过 $2 \cdot 10^5$（即 $\sum\limits_{i=1}^{m} k_i \le 2 \cdot 10^5$）。

For each query, print the answer — "YES", if there is a path from the root to some vertex $u$ such that each of the given $k$ vertices is either belongs to this path or has the distance $1$ to some vertex of this path and "NO" otherwise.

对于每个查询，请输出答案——如果存在一条从根节点到某个顶点 $u$ 的路径，使得给定的 $k$ 个顶点中的每一个要么属于该路径，要么与该路径上的某个顶点的距离为 $1$，则输出 "YES"；否则输出 "NO"。

The picture corresponding to the example:

Consider the queries.

The first query is $[3, 8, 9, 10]$. The answer is "YES" as you can choose the path from the root $1$ to the vertex $u=10$. Then vertices $[3, 9, 10]$ belong to the path from $1$ to $10$ and the vertex $8$ has distance $1$ to the vertex $7$ which also belongs to this path.

The second query is $[2, 4, 6]$. The answer is "YES" as you can choose the path to the vertex $u=2$. Then the vertex $4$ has distance $1$ to the vertex $1$ which belongs to this path and the vertex $6$ has distance $1$ to the vertex $2$ which belongs to this path.

The third query is $[2, 1, 5]$. The answer is "YES" as you can choose the path to the vertex $u=5$ and all vertices of the query belong to this path.

The fourth query is $[4, 8, 2]$. The answer is "YES" as you can choose the path to the vertex $u=9$ so vertices $2$ and $4$ both have distance $1$ to the vertex $1$ which belongs to this path and the vertex $8$ has distance $1$ to the vertex $7$ which belongs to this path.

The fifth and the sixth queries both have answer "NO" because you cannot choose suitable vertex $u$.

对应示例的图片：

考虑如下查询。

第一个查询为 $[3, 8, 9, 10]$。答案为“YES”，因为你可以选择从根节点 $1$ 到顶点 $u=10$ 的路径。此时，顶点 $[3, 9, 10]$ 均属于从 $1$ 到 $10$ 的路径，而顶点 $8$ 到该路径上的顶点 $7$ 的距离为 $1$。

第二个查询为 $[2, 4, 6]$。答案为“YES”，因为你可以选择到顶点 $u=2$ 的路径。此时，顶点 $4$ 到该路径上的顶点 $1$ 的距离为 $1$，而顶点 $6$ 到该路径上的顶点 $2$ 的距离也为 $1$。

第三个查询为 $[2, 1, 5]$。答案为“YES”，因为你可以选择到顶点 $u=5$ 的路径，且查询中的所有顶点均属于该路径。

第四个查询为 $[4, 8, 2]$。答案为“YES”，因为你可以选择到顶点 $u=9$ 的路径，此时顶点 $2$ 和 $4$ 到该路径上的顶点 $1$ 的距离均为 $1$，而顶点 $8$ 到该路径上的顶点 $7$ 的距离也为 $1$。

第五个和第六个查询的答案均为“NO”，因为你无法选出满足条件的顶点 $u$。